Analysis of the mechanical behavior of functional gradient porous plates on an elastic foundation

Summary: This study presents an in-depth analysis of the bending behavior of porous functionally graded material (P-FGM) plates resting on a Winkler–Pasternak elastic foundation. Two types of transverse loading are considered: uniform and sinusoidal. The theoretical framework relies on a refined shear deformation formulation based on a trigonometric function, and the equilibrium equations are established using the principle of virtual work, then solved analytically via Navier's method.To better reflect recent phenomena related to porosity and foundation–structure interaction, the study incorporates a non-uniform logarithmic distribution of porosity, allowing for the simulation of complex configurations encountered in practice. This approach also highlights several nonlinear behaviors characteristic of porous FG plates.The parametric study focuses on the combined effect of several factors on the mechanical response: porosity ratio (ξ), foundation parameters (kw,ks), power-law index (k), aspect ratio (a/b), and thickness ratio (a/h). The results show that increasing porosity significantly reduces the material stiffness, while elastic foundations help compensate for this weakening by limiting deformations, especially in thin plates.It was clearly observed that increasing the porosity ratio ξ leads to a marked reduction in stiffness, particularly in the central zone of the plate an effect amplified by high values of the power-law index k. This central concentration of porosity, typical of logarithmic distributions, induces significant mechanical weakening and strongly nonlinear responses. However, Winkler–Pasternak-type foundations (kw,ks) optimize this distribution by enhancing load diffusion, limiting deformations, reducing deflections and stresses, and thus improving overall structural efficiency. Moreover, an increase in stiffness observed near the plate edges for certain ξ values reveals an unexpected phenomenon of localized reinforcement. These observations highlight the high sensitivity of porous FGM plates to the combined parameters ξ and k, underlining the importance of accurate modeling in predicting their mechanical behavior.Consequently, the proposed theoretical approach proves to be both accurate, efficient, and computationally inexpensive in predicting the mechanical responses of FGM plates resting on elastic foundations. These results represent a significant advance in the modeling of porous structures, contributing to structural optimization.